The number of possible min-heaps containing each value from {1, 2, 3, 4, 5, 6, 7} exactly once is _______. Note –This was Numerical Type question.
(A)80
8
(C)20
210
Answer:(A)
Explanation:
Explanation:
Set minimum element as root (i.e 1), now 6 are remaining and left subtree will have 3 elements, each left subtree combination can be permuted in 2! ways. Total ways to design min-heap with 7-elements =
Alternative approach –
Total number of min or max heap tree with 1 to N elements are using recurrence relation:
T(N) =(N-1)Ck * T(k) * T(N-k-1), where k = number of nodes on left subtree T(1) = 1 T(2) = 1 T(3) = 2 T(4) = 3C2 * T(2) * T(1) = 3 T(5) = 4C3 * T(3) * T(1) = 8 T(6) = 5C3 * T(3) * T(2) = 20 T(7) = 6C3 * T(3) * T(3) = 80
So, answer is 80.
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